A generalization of Lelieuvre's formula to equiaffine immersions of general codimension

摘要

A non-degenerate equiafflne immersion of codimension one into an equiaffine space is locally expressed in terms of its conormal map and its affine fundamental form. The expression is called the Lelieuvre's formula, We recently defined the notions of an equiafflne immersion of general codimension and its transversal volume element map. In this paper, we locally express a non-degenerate equiaffine immersion of general codimension into an equiafflne space in terms of its transversal volume element map and its affine fundamental form.